Some Studies on Semirings and Ordered Semrings

Semirings abound in the mathematical world around us. The first mathematical structure we encounter-the set of natural numbers is a semiring. Other semirings arise naturally in such diverse areas of mathematics as combinatorics functional analysis topology graph theory Euclidean geometry probability theory commutative and non-commutative ring theory optimization theory discrete event dynamical systems automata theory formal language theory and the mathematical modeling of quantum physics and parallel computation systems.